Omega 34 (2006) 562–570www.elsevier.com/locate/omega

Remanufacturing of mobile phones—capacity, program andfacility adaptation planning

C. Franke∗, B. Basdere, M. Ciupek, S. SeligerInstitute for Machine Tools and Factory Management, Technical University Berlin, Department of Assembly Technology and Factory

Management, Pascalstr. 8-9, PTZ II, 10587 Berlin, Germany

Accepted 2 December 2004Available online 23 March 2005

Abstract

Successful remanufacturing of mobile phones must meet the challenges of continuously falling prices for new phonemodels, short life cycles, disassembly of unfriendly designs and prohibiting transport, labor and machining costs in high-wagecountries. A generic remanufacturing plan for mobile phones is developed. For the planning of remanufacturing capacitiesand production programs, a linear optimization model is introduced. To support the planner in the periodic adaptation of anexisting remanufacturing facility under quickly changing product, process, and market constraints, discrete-event simulationis applied. Uncertainties regarding quantity and conditions of mobile phones, reliability of capacities, processing times, anddemand are considered. The simulation model is generated by an algorithm using results from the linear optimization approach.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Mobile phone remanufacturing; Production program planning; Linear optimization; Discrete-event simulation

1. Introduction

Today, the remanufacturing of expensive, long-living in-vestment goods, e.g. machine tools, jet fans, military equip-ment or automobile engines, is extended to a large num-ber of consumer goods with short life cycles and relativelylow values. Reuse is an alternative to material recycling tocomply with recovery rates and quantities as well as specialtreatment requirements as prescribed by European legisla-tion with the directive on Waste of Electrical and ElectronicEquipment (WEEE) [1,2].

Some remanufacturing cases are widely known, e.g. theremanufacturing of single use cameras (Eastman Kodak andFuji Film), toner cartridges (Xerox), photocopiers (Fuji Xe-rox, Australia, Netherlands and UK), commercial cleaningequipment (Electrolux) and brand name computers (IBM,France, Germany, USA; HP, Australia). Remanufacturers

∗ Corresponding author. Fax.: +49 30 31422759.E-mail address: cfranke@mf.tu-berlin.de (C. Franke).

0305-0483/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.omega.2005.01.016

are OEMs themselves who have integrated new distributionmodels such as leasing or “pay per use” with remanufac-turing strategies [3]. Other remanufacturing practices, e.g.for washing machines (ENVIE, France), personal comput-ers (ReUse network, Germany), accumulators (teldeon, Ger-many), cordless phones, car stereos, FM radios (Topp Com-panies, USA) and mobile phones (ReCellular, USA; GreenerSolutions, UK) are less popular, due to the fact that OEMsare not involved. Products are not sold through regular retailchannels established by OEMs.

Market studies regarding offer and demand for mobilephones with GSM standard [1,4,5] show the worldwide po-tential for mobile phone remanufacturing. The studies re-vealed that with a total quantity of over 200 Mio. unutilizedmobile phones, Europe can serve as a supply market. De-mand markets can be found in Asia and Latin America, e.g.,China and Brasil, where market penetration is as low as 20%and—in the case of Brasil—where the old TDMA mobilecommunication standard is currently replaced by the GSMstandard. By means of low-cost remanufactured phones, one

C. Franke et al. / Omega 34 (2006) 562–570 563

cannot only serve communication demands of lower incomeclasses in those regions, but it is possible to recycle phonescomplying with WEEE requirements and thus provide ser-vices for OEMs within the scope of the directive.

In order to evolve mobile phone remanufacturing into aprofitable business segment, it is necessary to provide re-manufacturers with efficient planning methods and tools, ca-pable to deal with the special procurement, remanufacturingand distribution processes. The tools and methods shouldallow the efficient reconfiguration of remanufacturing facil-ities considering fast-changing product, process, and marketconditions. The most frequently changing input parametersare the type and quantity of mobile phones offered at themarket. In Western Europe, with the average replacement cy-cle of phones being less than 18 months and more than 100new phone models every year it is feasible to assume that theremanufacturing program requires adaptation several timesduring a year [5]. In this paper, an approach is presentedto support the remanufacturing program planning under theabove-stated framework. The remanufacturing program andrequired capacities are determined by means of combinato-rial optimization. Based on the results, the planner is enabledto adapt and evaluate the existing remanufacturing facilityusing discrete-event simulation.

2. Constraints for planning of mobile phoneremanufacturing

In the following, the process chain of mobile phone re-manufacturing is analyzed to identify aspects that need tobe considered in the planning of a remanufacturing facil-ity. The procurement of phones can be realized in coopera-tion with OEMs, e.g. by acquisition of overproduction, or incooperation with net providers, supermarkets or other pri-vate and public organizations who have frequent and closecontact with phone users, in so-called take backs. Experi-ence has shown that consumers are willing to either turnin their used phones as a charitable donation or trade themin for benefits such as free phone minutes [6,4]. An effec-tive and efficient take back of mobile phones is an essentialelement of the remanufacturing process chain. Legislationhas a strong influence on why and how take back is andwill be organized for different product classes. Yet, in manycases, take back is accomplished without any pressure beingbuilt up by governments. This is the case if profits expectedfrom selling remanufactured products or recycled materialcan compensate the costs for take back, inspection, testing,refurbishment and redistribution of products. Using retailchannels for product take back is an adequate approach toutilize existing logistics capacities, and address known cus-tomers to replace their used products. The lower the takeback costs in relation to the residual value of the product,the higher are the chances for voluntary take back withoutthe need for legal regulations. If the residual value is eitherlow or not known to the user, and weight and volume permit

Fig. 1. Automated disassembly of mobile phones [11].

disposal together with domestic waste, the risk of incorrectdisposal of the product is relatively high. For these typesof products, it is necessary to implement a take back offer-ing some benefit to the user. In take backs, the variabilityregarding quantity, model and condition of returned mobilephones is high. Identification and pre-sorting of phones atcollection points can reduce volume and model diversity ofphones sent to the remanufacturing facility.

After the take back, phones need to be separated, e.g. fromchargers or earphones, and identified. Experience of reman-ufacturers shows that about 70% of phones recovered in Eu-rope and the USA are considered beyond economic reuse,i.e. that either remanufacturing costs are too high or demandis too low for these phones, and they are consequently sentto material recycling [6,4]. The remaining phones need tobe tested to determine optical or functional faults that canbe ascribed to the main elements housing, printed circuitboard (PCB), display, microphone and speaker. The combi-nation of faults results in different process times for disas-sembly and reassembly. Replacement components are sup-plied either by external procurement or internal retrieval ofcomponents from used phones.

Efficient disassembly is a prerequisite for the remanu-facturing of phones with functional faults. The disassemblyprocess of none-flip (candy bar) mobile phones can be auto-mated, making use of a flexible disassembly cell developedwithin the Collaborative Research Center 281 “Disassem-bly Factories” [7,8] depicted in Fig. 1. The hybrid systemis characterized by the integration of manual and automatedoperations. In this system, the only manual operation is theremoval of the main battery. For the automated operations, a4-axis Scara robot was applied. A flexible gripper is used topick cell phones independent of length and width. It placesthe phone in a flexible clamping device. Pneumatic cylin-ders are used to form the specific shape of the phone, thusbeing able to grip independent of the provided phone geom-etry. The clamping device attached to a pivot arm ensuresthe time efficient removal of non-ridged part, such as the key

564 C. Franke et al. / Omega 34 (2006) 562–570

pad, by rotatory movement. Cell phones with exchangeablefront housing covers usually provide snap fits to attach thefront housing to the back housing. A vacuum gripper with aspecially shaped spike is used to open these snap fits and toremove the front housing. A commercial screwing spindle,operated in left-hand motion is used to remove the screws.Most commonly, screws of the type Torx 5 are used. Thesystem needs to be programmed individually for each phonemodel, making its application especially suitable for modelsavailable at high quantities.

Experience of mobile phone remanufacturing in the USAhas shown that customers are willing to remunerate valueadding upgrades of phones, e.g. software update or surfacetreatment by polishing. Offering different quality classes forthe same phone model is an approach to meet the marketdemand. Customers show more flexibility in accepting al-ternative phone models as substitutes, as long as they offercomparable features, such as software updates. A more elas-tic demand for mobile phones simplifies the handling of thehigh variability on the phone procurement side. Future de-mand could also come from OEMs or independent serviceentities procuring retrieved phone components to cope withpost-production supply, i.e. the supply of spare parts to cus-tomers and service networks beyond the time of the produc-tion of the product. Recovering components could help toreduce warehousing of large quantities of spare parts overlong periods of time, in order to reduce the extent of thecontinuing production of spare parts.

3. Generic remanufacturing process chain

To enable meeting a cost-efficient treatment decision foreach phone, a generic remanufacturing process was modeled(Fig. 2). Options for phone utilization are reuse, componentsretrieval and material recycling. In case of reuse, three dif-ferent quality classes are differentiated, according to the ex-tent of remanufacturing. Upon arrival, phones are separatedfrom accessories and identified. Accessories, e.g. chargersor earphones, are identified and tested to assign them toreuse or recycling. Following identification, phones can besent directly to recycling or can be tested. Faultless mobilephones are assigned to either reuse (ReMobile Class1) orsoftware update. Updated phones can be assigned to eitherreuse (ReMobile Class2) or polishing (ReMobile Class3).Defective phones are assigned to alternatively manual orautomated disassembly, cleaning and reassembly. Hereafter,phones can undergo additional value-adding processes, i.e.software update or polishing, or be sent directly to reuse.

When deciding which phones are to be assigned to whichprocess, certain constraints, e.g. the availability of, and de-mand for phones and components, the condition of avail-able phones or the cost for and number of remanufacturingresources need to be considered. Due to the high numberof existing phone variants at the market—more than 800,including software variants more than 2000—and the diver-

Hm,z

HTm,zHY m,z

HTY m,z

HRm,z

HRU m,z

HTU m,z

HTS m,z

HRS m,z

HSUm,zHPUm,z

HPUm,z

HDMm,zHDAm,z

HCMm,zHCAm,z

HCMm,zHCAm,z

Identification (R4)Mobile Phones

Test (R5)

ManualDisassembly (R2)

AutomatedDisassembly (R1)

Cleaning (R6)Reassembly (R3)

HDMm,zHDAm,z

SoftwareUpdate (R7)

Polish (R8)

Sorting

IdentificationAccessories

Take back

Test

Hm,z / A

A

Packaging

NewAccessories

NewComponents

HX Mobile Phones C ComponentsA Accessories

Decision

Legend

Material Flow

ReMobile

ReCover

Class1

Components

ReMobile

ReMobile

ReMobile

Class 1

Recycling

Class 2

Class 3

C

C

A

+CYc

CUc

Fig. 2. Optional phone treatment.

sity of phone conditions, process complexity is high. Theproblem of assigning each phone to a cost optimal treatmentbelongs to the class of combinatorial optimization. Com-binatorial optimization deals with models and methods tofind the best solution for problems with discrete choices,and is well established in disassembly planning [9]. In thedescribed problem, the discrete choices are related to thediscrete amount of required capacities for remanufacturingprocesses and the discrete number of mobile phones whichare assigned to every remanufacturing process.

4. Model for capacity and program planning

Based on the generic remanufacturing process, a math-ematical model was developed to determine the requiredprocess capacities for identification, testing, manual or

C. Franke et al. / Omega 34 (2006) 562–570 565

Table 1Definition of derived sets used in Fig. 2

Hm,z quantity of all available phones (H)HTm,z quantity of phones (H) assigned to testing (T)HYm,z quantity of phones (H) assigned to recycling (Y)HTYm,z quantity of phones (H) tested (T) and assigned to recycling (Y)HTUm,z quantity of phones (H) tested (T) and assigned to reuse (U)HDAm,z quantity of phones (H) to be recovered (D) that are assigned to automated disassembly (A)HCAm,z quantity of phones (H) of which components shall be recovered (C) that are assigned to automated disassembly (A)HDMm,z quantity of phones (H) to be recovered (D) that are assigned to manual disassembly (M)HCMm,z quantity of phones (H) of which components shall be recovered (C) that are assigned to manual disassembly (M)HRm,z quantity of phones (H) assigned to cleaning and reassembly (R)CUc quantity of components (C) assigned to reuse (U)CYc quantity of components (C) assigned to recycling (Y)HRUm,z quantity of phones (H) cleaned and reassembled (R) assigned to reuse (U)HRSm,z quantity of phones (H) cleaned and reassembled (R) assigned to software update (S)HTSm,z quantity of phones (H) tested (T) assigned to software update (S)HSUm,z quantity of phones (H) software updated (S) that are assigned to reuse (U)HPUm,z quantity of phones (H) assigned to polishing (P) and thereafter assigned to reuse (U)

automated disassembly, reassembly, software update, andpolishing for a given number of offered and demandedmobile phones. Available product, process and market dataare considered regarding product structure and conditionof used phones, operating times for remanufacturing pro-cesses, capacities of resources, offer for used phones anddemand and revenues for sold phones and components aswell as costs for assigned process capacities.

Fig. 2 represents all assignment options for products, andall types of remanufacturing resources considered in thismodel. Abbreviations used in Fig. 2 are described in Table1 . For example, the decision variable HTm,z describes thequantity of the mobile phone type m with the condition zthat is assigned to the process testing after being identified,whereas HYm,z represents the quantity of the mobile phonetype m with the condition z that is assigned to recycling.All assigned mobile phone quantities are defined as non-negative integers.

The following sets are used in the model:

Set of mobile phones: M; M = {1, . . . , i}; index m ∈ M .

Set of components: C; C = {1, . . . , j}; index c ∈ C.

Set of conditions: Z; Z = {1, . . . , k}; index z ∈ Z.

Set of resources: R; R = {1, . . . , l}; index r ∈ R.

Set of processes: P; P = {1, . . . , n}; index p ∈ P .

Analyzed phones can have different conditions regardingthe functionality of the five basic mobile phone components,i.e. housing, PCB, display, speaker, and microphone. In thismodel, only two conditions for each component—functionaland non-functional—are considered resulting in 32 (=25)

possible phone conditions. Data about the failure prob-

ability of mobile phone components is available from marketsurveys.

The objective in this approach is to maximize the profitmargin considering revenues for material recycling RYm,components reuse RCUc and phone reuse, i.e. ReMobileClasses I–III RUIm, RUIIm, RUIIIm, as well as costs CRr

for installed resources RQr .

MAX

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

∑m

RYm × HYm,z+∑m

∑z

RYm × HTYm,z+∑m

∑z

∑c

RCUc × CUc+∑m

∑z

RUIm × (HTUm,z+HRUm,z)+

∑m

∑z

RUIIm × HSUm,z+∑m

∑z

RUIIIm × HPUm,z−∑r

CRr × RQr

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

. (1)

The solution is being derived under consideration of con-straints for material flow continuity, available resource ca-pacity, and the demand and offer for phones and components(see Appendix).

5. Implementation

The developed capacity and program planning model isdescribed as a combinatorial optimization problem. To solvethis type of problem, two classes of methods can be distin-guished: exact methods that guarantee an optimal solutionand heuristic methods, without any a priori guarantee in

566 C. Franke et al. / Omega 34 (2006) 562–570

terms of solution quality. Exact methods apply mainly treesearch technique with complete enumeration and boundedenumeration. For bounded enumeration, the branch & boundalgorithm has been proved to find the optimal solution, yetwith non-polynomial running time behavior [10]. In recentyears, efficient meta heuristic search methods, e.g. GeneticAlgorithms, Evolutionary Strategies, Simulated Annealing,Threshold Accepting and Tabu Search for formulation andsolution of complex, reality-based problems have been de-veloped. These heuristics are mainly applied for problems,where enumeration methods would require extremely longcomputation time, to find the optimal solution. The selectionof an adequate method deals with the trade off between so-lution quality and computation time. Also, the selection ofa method depends on the time available for the implemen-tation of the model, and the necessity of adapting the modeldue to frequently changing decision variables or constraintsin the decision problem. In this approach, modifications ofthe described problem like remanufacturing technologies orpossible material flow alternatives are very probable. If theproblem complexity described by number of decision vari-ables and constraints allows the application of enumerationmethods, it is advantageous to use standard solvers, e.g.CPLEX, GAMS or LINGO. These solvers are using branch& bound algorithms to find the optimal solution, accordingto the applied data. Solvers provide a modeling languagefor a fast implementation of the developed mathematicalmodel. The developed Integer Linear Programming (ILP)model was implemented using the solver LINGO.

In order to reduce the computation time of the imple-mented ILP-model with a large number of variants, phonesneed to be grouped in homogeneous classes. An adequatemethod to sort objects into classes, or clusters according toproduct and process attributes is the cluster analysis, beinga widely applied tool in disassembly planning [11]. Hierar-chical clustering is applied to determine the optimal numberof clusters. The basis for the classification is a set of objectsdescribed by attributes to calculate its distances, i.e. theirsimilarities. The challenge of the cluster analysis is to de-fine and to scale disassembly relevant attributes. Three dif-ferent scales are differentiated: binary scales, e.g. functionalor non-functional components, metric scales, e.g. process-ing time, and indirect scales, e.g. to describe the precedenceof disassembly steps.

In this approach market, product and process attributes ofmobile phone models are considered. Parameter values forthe product attribute “Probability of failure [%]” of compo-nent X, and the process attribute “Disassembly automated[s]” are dependent on the condition of the phone. Accord-ing to these attributes, phones tend to belong to one clusterwhen they show similar failure patterns or require equallylong processing times for disassembly of faulty components.Values for the market attribute “Value [¥] (remanufactured)”,and the process attribute “Testing [s]”, are not dependent onthe condition of the phone. Products that generate compa-rable retail values and cause similar remanufacturing costs

……

Display

Printed CircuitBoard

Housing

Speaker

Microphone

none

Con

ditio

n(d

efec

tive

com

pone

nts)

N 6210

N 7650

C 35i

S 42

A 60

Market, product and process attributes

Age

[mon

ths]

Val

ue [

] (r

eman

ufac

ture

d)

Dis

asse

mbl

yau

tom

ated

[s]

Dis

asse

mbl

ym

anua

l [s]

Test

ing

[s]

… …

Pro

babi

lity

[%]

Rea

ssem

bly

[s]

Mobile P

hone Models

40

20

15

25

15

10

36 25 210

0 0

40 30 25

45 40 35

60 50 40

10 5 5

10 5 5

……

……

……

……

……

0

Fig. 3. Attributes for clustering of mobile phones.

are likely to belong to one cluster. Fig. 3 depicts attributesand exemplary parameter values. All depicted variables aremetrically scaled.

In this approach, attributes are normalized using the z-transformation. A combination of the squared Euclidean dis-tance function and the single linkage algorithm is used togroup mobile phones in clusters.

Subsequent to grouping mobile phones in clusters, a rep-resentative phone needs to be determined for each cluster.The phone with the highest market share in each clusteris selected as the representative product. The product, pro-cess and market attributes of this representative will be usedby the developed ILP model. The determined capacities foreach remanufacturing process are required input values forthe adaptation of the remanufacturing facility.

6. Facility planning and evaluation

To support the planner in the periodic adaptation of anexisting remanufacturing system he needs to be enabled toapply the results from the capacity and program planningmodel efficiently. The exemplary model of a remanufactur-ing facility depicted in Fig. 4 is dimensioned for the reman-ufacturing of two million mobile phones per year represent-ing 25% of the German market potential for idle phones.Mobile phones from the five main producers, Nokia, Mo-torola, Samsung, Siemens and SonyEricsson are being con-sidered, representing about 90% market share. The informa-tion regarding the resources required for remanufacturingare determined by the application of the ILP model. Thecapacities are represented by the number of required work

C. Franke et al. / Omega 34 (2006) 562–570 567

Fig. 4. Steps for remanufacturing facility design.

stations in the factory under the assumption of a two-shiftoperation and 250 working days per year. The performanceanalysis of the simulation model confirmed the required av-erage daily performance of 8000 mobile phones.

Data for identification, testing and manual as well as au-tomated disassembly of different mobile phones was exper-imentally determined. As shown in Table 2, process timeswere taken for automated disassembly as well as manual dis-

assembly operations. The processing times of the automatedoperations are about 170% of the manual ones. Most of thesurplus results from the tool changes necessary. Integratingall tools in one would lead to savings as shown in Table 2.Taking into account the high labor costs in European coun-tries, automated disassembly could be economically com-petitive with manual disassembly, despite the slightly higheroperation times.

568 C. Franke et al. / Omega 34 (2006) 562–570

Table 2Disassembly process time

Automated disassembly Manual disassembly

Nr. Tool Nr. Operation Primary Secondary Savingsprocess process possible

1 1 Identification of Barcode 2.02 2 Pick and place in clamping device 5.4 9.3 2.53 3 Removal of housing cover 5.8 11.6 9.64 4 Unscrewing 4× screw Torx 5 PWB 55.9 17.8 11.05 5 Rotation of clamp 2.06 4 Unscrewing 2× screw Torx 5 of display PWB 25.8 4.0 4.17 3 Removal of display PWB 2.6 26.6 18.78 4 Unscrewing 1× screw Torx 5 PWB 11.9 2.5 2.19 3 Removal of PWB 2.8 17.0 9.9

Total 164.3 34.8 98

Tools:1 = CCD vision system fix mounted 2 = Flexible gripper 3 = Vacuum gripper

The selected testing and disassembly equipment is suitedfor the daily capacity of 8000 phones. Based on the se-lected equipment, process times and process costs were de-termined. The data is only viable for comparable operationsof the same size. Economies of scale do have an impact onthe selection of equipment and thus on process times andcosts. Discontinuities should be expected in cost functionsfor warehousing of inventory, as warehousing concepts usu-ally differ depending on the quantities handled. In this ap-proach, costs for warehousing, logistics, and other generaland administrative costs are not accounted for.

The exemplary model consists of storage areas for phonesand accessories received, new components and shipmentas well as intermediate storages for tested and identifiedphones and accessories. Transport between remanufacturingprocesses and storage areas is manual, the linkage of re-manufacturing resources is automated using conveyors. Themodel considers every process from the developed genericremanufacturing process chain. The capacities are deter-mined by the ILP model results. To determine the changesregarding the required storage and transportation capacitiesand analyze the performance of the remanufacturing facilityunder consideration of uncertainties regarding quantity andconditions of mobile phones, reliability of capacities, pro-cessing times, and demand, simulation is applied. Discreteevent simulation has proven to be an effective and efficienttool for the analysis of disassembly and remanufacturingsystems [12,13].

In order to increase the efficiency, simulation models needto be generated automatically under consideration of the re-sults derived by the ILP model. For this purpose, the ob-ject oriented simulation tool eM-Plant was selected. Thesoftware allows to generate and configure predefined objectclasses, e.g. storage and conveyor systems, remanufactur-

ing resources, and workers. The developed algorithm for thedata driven generation of remanufacturing facility modelscreates entities of these object classes and forms an exe-cutable simulation model. The required data for the entityconfiguration is imported via the Open DataBase Connectiv-ity (ODBC) interface from a database where the ILP modelresults as well as the given model structure of a remanufac-turing facility are stored. Fig. 4 shows the steps, requireddata and used software for adaptation and evaluation of amobile phone remanufacturing facility.

The developed methods, models and data structures sup-port a fast and continuous adaptation of remanufacturingfacilities under quickly changing product, process, and mar-ket constraints. By applying the proposed approach, a man-ually enhanced simulation model of a remanufacturing fa-cility can be built and analyzed within a day. However, aconducted sensitivity analysis clarified the enormous sensi-tivity of the factory with respect to the processing time fordis- and reassembly and the quality of the incoming mobilephones. This demonstrates the challenges in the planning ofa remanufacturing factory for mobile phones, in particularagainst the background that there is no firm data about theamount and quality of mobile phones offered at the market.

7. Conclusion and outlook

The presented approach for capacity and remanufactur-ing program planning by means of combinatorial optimiza-tion and discrete-event simulation supports the planner inthe periodic adaptation of an existing remanufacturing sys-tem. The process capacities and the remanufacturing pro-gram are determined by the optimization model. Based onthese results, an executable simulation model is generated

C. Franke et al. / Omega 34 (2006) 562–570 569

automatically for the remanufacturing system consideringprocess capacities, and resources for transport and storage.The simulation model allows the planner to determine therequired transport and storage capacities, and the perfor-mance of the remanufacturing system.

Further research will analyze which factory elements, e.g.transport systems, can be planned using the combinatorialoptimization approach, without increasing the complexityof the model significantly. Other possible extensions of theapproach are the consideration of additional processes, e.g.the treatment of accessories, or the updating of software as aresponse to “software failure” due to malfunctioning PCBs.Also, the supply of replacement components for remanu-facturing should be differentiated into internal supply fromcomponents retrieval and external procurement to accountfor the different costs involved. Additional destructive dis-assembly operations could be considered prior to sendingmobile phones to material recycling to comply with require-ments of the WEEE, i.e. to fulfill the mandatory disassemblyof PCBs and batteries before shredding.

Acknowledgements

This paper presents results of the CRC 281 financed bythe Deutsche Forschungsgemeinschaft (DFG).

Appendix

According to Fig. 2, constraints (2)–(7) guarantee materialflow continuity for the remanufacturing program:

Hm,z = HTm,z + HYm,z ∀m, ∀z, (2)

HTm,z = HTYm,z + HCMm,z + HCAm,z + HTUm,z

+ HTSm,z + HDMm,z + HDAm,z

∀m, ∀z, (3)

HRm,z = HDMm,z + HDAm,z ∀m, ∀z, (4)

HRm,z = HRSm,z + HRUm,z ∀m, ∀z, (5)

HTSm,z + HRSm,z = HSUm,z + HPUm,z ∀m, ∀z, (6)

HTSm,z + HTUm,z = 0 ∀m, ∀z�2. (7)

Resources required to perform remanufacturing processesare assigned under consideration of the previously stated re-quirements of the remanufacturing program. Decision vari-ables for resource capacities need to be defined as non-negative integers as only whole resources can be assigned.Constraint (8) guarantees that the capacity RCr of all as-signed automated disassembly stations RQr is sufficient forthe disassembly of all phones assigned to these stations. Thedisassembly time DATm,z required for the automated disas-sembly of the mobile phone type m with a certain condition

z is derived by test disassemblies∑m

∑z

(HDAm,z + HCAm,z) × DATm,z �RQr × RCr

∀r = 1. (8)

Analogical, constraint (9) guarantees the required resourcecapacity for manual disassembly, with DMTm,z being thedisassembly time required for the manual disassembly of aphone with a certain condition:∑m

∑z

(HDMm,z + HCMm,z) × DMTm,z �RQr × RCr

∀r = 2. (9)

Whether or not a disassembly process of a phone can be au-tomated or not is described by the binary variable Bm, withBm = 1 indicating that automation is possible. Constraints(10) and (11) guarantee that no phones are assigned to au-tomated disassembly if Bm = 0.∑z

HDAm,z = 0 ∀m|Bm = 0, (10)

∑z

HCAm,z = 0 ∀m|Bm = 0. (11)

Constraint (12) assures the required reassembly capacity,considering the time required for reassembly RMTm,z:∑m

∑z

HRm,z × RMTm,z �RQr × RCr ∀r = 3. (12)

Constraints (13)–(17) guarantee resource capacities for iden-tification (13), testing (14), cleaning (15), software update(16), and polishing (17). The process time PTm,p dependson the phone type m, not on the condition z:∑m

∑z

Hm,z × PTm,p �RQr × RCr

∀p = 1, ∀r = 4, (13)∑m

∑z

HTm,z × PTm,p �RQr × RCr

∀p = 2, ∀r = 5, (14)∑m

∑z

HRm,z × PTm,p �ROr × RCr

∀p = 3, ∀r = 6, (15)∑m

∑z

(HRSm,z + HTSm,z) × PTm,p �RQr × RCr

∀p = 4, ∀r = 7, (16)∑m

∑z

HPUm,z × PTm,p �RQr × RCr

∀p = 5, ∀r = 8. (17)

The market driven demands for phones and components arebeing considered in constraints (18)–(22). Constraint (18)determines the type and quantity of components that can be

570 C. Franke et al. / Omega 34 (2006) 562–570

obtained by manual and automated disassembly of phonesassigned to component recovery, and assigns components tomaterial recycling CYc or to the components for reuse classReCover CUc. BCOm,z,c is the binary variable describingwhich functional component c can be obtained from phonetype m with a certain condition z. Constraints (19) guaranteethat the quantity of sold components CUc is not higher thanthe corresponding demand DCOc:∑m

∑z

(HCMm,z + HCAm,z) × BCOm,z,c

= CYc + CUc ∀c, (18)

CUc �DCOc ∀c. (19)

Constraints (20)–(22) assure that the quantity of phones as-signed to ReMobile Classes I–III are smaller than the de-mand for these classes DUIm, DUIIm and DUIIIm:∑z

(HTUm,z + HRUm,z)�DUIm ∀m, (20)

∑z

HSUm,z �DUIIm ∀m, (21)

∑z

HPUm,z �DUIIIm ∀m. (22)

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